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<a href="_svm_problems_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> * </span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       -</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> *</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * \author      T. Glasmachers, O.Krause</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * \date        2013</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * </span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * </span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * </span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * </span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> *</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> */</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_QP_SVMPROBLEMS_H</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="preprocessor">#define SHARK_ALGORITHMS_QP_SVMPROBLEMS_H</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#include &lt;<a class="code" href="_box_constrained_problems_8h.html">shark/Algorithms/QP/BoxConstrainedProblems.h</a>&gt;</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a>{</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="comment">// Working-Set-Selection-Criteria are applied as follows:</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="comment">// Criterium crit;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="comment">// value = crit(problem, i, j);</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span>    </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span>    <span class="comment"></span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="comment">///\brief Computes the most violating pair of the problem</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment">///</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">/// The MVP is defined as the set of indices (i,j)</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// such that g(i) - g(j) is maximal and alpha_i &lt; max_j</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// and alpha_j &gt; min_j.</span></div>
<div class="foldopen" id="foldopen00047" data-start="{" data-end="};">
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="structshark_1_1_m_v_p_selection_criterion.html">   47</a></span><span class="comment"></span><span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_m_v_p_selection_criterion.html" title="Computes the most violating pair of the problem.">MVPSelectionCriterion</a>{<span class="comment"></span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">    /// \brief Select the most violating pair (MVP)</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">    /// \return maximal KKT violation</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment">    /// \param problem the SVM problem to select the working set for</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span><span class="comment">    /// \param i  first working set component</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span><span class="comment">    /// \param j  second working set component</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="foldopen" id="foldopen00055" data-start="{" data-end="}">
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"><a class="line" href="structshark_1_1_m_v_p_selection_criterion.html#a68398922534566a9d2601d92096e4edc">   55</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_m_v_p_selection_criterion.html#a68398922534566a9d2601d92096e4edc" title="Select the most violating pair (MVP)">operator()</a>(Problem&amp; problem, std::size_t&amp; i, std::size_t&amp; j)</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span>    {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        <span class="keywordtype">double</span> largestUp = -1e100;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordtype">double</span> smallestDown = 1e100;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span> </div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <span class="keywordflow">for</span> (std::size_t a=0; a &lt; problem.active(); a++)</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>        {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            <span class="keywordtype">double</span> ga = problem.gradient(a);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>            <span class="keywordflow">if</span> (!problem.isUpperBound(a))</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>            {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                <span class="keywordflow">if</span> (ga &gt; largestUp)</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                    largestUp = ga;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span>                    i = a;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>                }</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>            }</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>            <span class="keywordflow">if</span> (!problem.isLowerBound(a))</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>            {</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>                <span class="keywordflow">if</span> (ga &lt; smallestDown)</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>                {</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>                    smallestDown = ga;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>                    j = a;</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>                }</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>            }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        }</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span> </div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>        <span class="comment">// MVP stopping condition</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        <span class="keywordflow">return</span> largestUp - smallestDown;</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>    }</div>
</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>    </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="structshark_1_1_m_v_p_selection_criterion.html#a2c9b635d190d337a2d3aaf454a77cb9d">   85</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="structshark_1_1_m_v_p_selection_criterion.html#a2c9b635d190d337a2d3aaf454a77cb9d">reset</a>(){}</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>};</div>
</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span> </div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span><span class="comment"></span> </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span><span class="comment">///\brief Computes the maximum gian solution</span></div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span><span class="comment">///</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span><span class="comment">/// The first index is chosen based on the maximum gradient (first index of MVP)</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span><span class="comment">/// and the second index is chosen such that the step of the corresponding alphas </span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span><span class="comment">/// produces the largest gain.</span></div>
<div class="foldopen" id="foldopen00094" data-start="{" data-end="};">
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="structshark_1_1_lib_s_v_m_selection_criterion.html">   94</a></span><span class="comment"></span><span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_lib_s_v_m_selection_criterion.html" title="Computes the maximum gian solution.">LibSVMSelectionCriterion</a>{</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>    <span class="comment"></span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span><span class="comment">    /// \brief Select a working set according to the second order algorithm of LIBSVM 2.8</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span><span class="comment">    /// \return maximal KKT vioation</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span><span class="comment">    /// \param problem the svm problem to select the working set for</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span><span class="comment">    /// \param i  first working set component</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span><span class="comment">    /// \param j  second working set component</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="foldopen" id="foldopen00103" data-start="{" data-end="}">
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="structshark_1_1_lib_s_v_m_selection_criterion.html#a84b251c8ca0ef80fe224866063d25fc4">  103</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_lib_s_v_m_selection_criterion.html#a84b251c8ca0ef80fe224866063d25fc4" title="Select a working set according to the second order algorithm of LIBSVM 2.8.">operator()</a>(Problem&amp; problem, std::size_t&amp; i, std::size_t&amp; j)</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>    {</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>        i = 0;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>        j = 1;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>        <span class="keywordtype">double</span> smallestDown = 1e100;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>        <span class="keywordtype">double</span> largestUp = -1e100;</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>        <span class="keywordflow">for</span> (std::size_t a=0; a &lt; problem.active(); a++)</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>        {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            <span class="keywordtype">double</span> ga = problem.gradient(a);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>            <span class="comment">//if (aa &lt; problem.boxMax(a))</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            <span class="keywordflow">if</span> (!problem.isUpperBound(a))</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>            {</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>                <span class="keywordflow">if</span> (ga &gt; largestUp)</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>                {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>                    largestUp = ga;</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>                    i = a;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>                }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            }</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        }</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <span class="keywordflow">if</span> (largestUp == -1e100) <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>        <span class="comment">// find the second index using second order information</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>        <span class="keyword">typename</span> Problem::QpFloatType* q = problem.quadratic().row(i, 0, problem.active());</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        <span class="keywordtype">double</span> best = 0.0;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span>        <span class="keywordflow">for</span> (std::size_t a = 0; a &lt; problem.active(); a++){</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>            <span class="keywordtype">double</span> ga = problem.gradient(a);</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>            <span class="keywordflow">if</span> (!problem.isLowerBound(a))</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>            {</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>                smallestDown=std::min(smallestDown,ga);</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>                </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>                <span class="keywordtype">double</span> gain = detail::maximumGainQuadratic2DOnLine(</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>                    problem.diagonal(i),</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>                    problem.diagonal(a),</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>                    q[a],</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>                    largestUp,ga</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span>                );</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span>                <span class="keywordflow">if</span> (gain&gt; best)</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span>                {</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno">  143</span>                    best = gain;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>                    j = a;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>                }</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>            }</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>        }</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno">  149</span>        <span class="keywordflow">if</span> (best == 0.0) <span class="keywordflow">return</span> 0.0;        <span class="comment">// numerical accuracy reached :(</span></div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span> </div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span>        <span class="comment">// MVP stopping condition</span></div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span>        <span class="keywordflow">return</span> largestUp - smallestDown;</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span>    }</div>
</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span>    </div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"><a class="line" href="structshark_1_1_lib_s_v_m_selection_criterion.html#a3ea14cbcfedf57f2cd5a630f84a65b11">  155</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="structshark_1_1_lib_s_v_m_selection_criterion.html#a3ea14cbcfedf57f2cd5a630f84a65b11">reset</a>(){}</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span>};</div>
</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span> </div>
<div class="foldopen" id="foldopen00158" data-start="{" data-end="};">
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"><a class="line" href="classshark_1_1_h_m_g_selection_criterion.html">  158</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_h_m_g_selection_criterion.html">HMGSelectionCriterion</a>{</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"><a class="line" href="classshark_1_1_h_m_g_selection_criterion.html#ac808db7f292558e743cbe39564a1db22">  160</a></span>    <a class="code hl_function" href="classshark_1_1_h_m_g_selection_criterion.html#ac808db7f292558e743cbe39564a1db22">HMGSelectionCriterion</a>():useLibSVM(true),smallProblem(false){}</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span><span class="comment"></span> </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span><span class="comment">    /// \brief Select a working set according to the hybrid maximum gain (HMG) algorithm</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno">  164</span><span class="comment">    /// \return maximal KKT vioation</span></div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span><span class="comment">    /// \param problem the svm problem to select the working set for</span></div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span><span class="comment">    /// \param i  first working set component</span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span><span class="comment">    /// \param j  second working set component</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="foldopen" id="foldopen00169" data-start="{" data-end="}">
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"><a class="line" href="classshark_1_1_h_m_g_selection_criterion.html#ab5378debaa7a2147d37bc14edfb76bcc">  169</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_h_m_g_selection_criterion.html#ab5378debaa7a2147d37bc14edfb76bcc" title="Select a working set according to the hybrid maximum gain (HMG) algorithm.">operator()</a>(Problem&amp; problem, std::size_t&amp; i, std::size_t&amp; j)</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>    {</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>        <span class="keywordflow">if</span> (smallProblem || useLibSVM || isInCorner(problem))</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span>        {</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span>            useLibSVM = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno">  174</span>            <span class="keywordflow">if</span>(!smallProblem &amp;&amp; <a class="code hl_function" href="group__shark__globals.html#gae1f82613484173e9fe1a07960dabff63" title="Calculates x^2.">sqr</a>(problem.active()) &lt; problem.quadratic().getMaxCacheSize())</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span>                smallProblem = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span>            <a class="code hl_struct" href="structshark_1_1_lib_s_v_m_selection_criterion.html" title="Computes the maximum gian solution.">LibSVMSelectionCriterion</a> libSVMSelection;</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span>            <span class="keywordtype">double</span> value = libSVMSelection(problem,i, j);</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span>            last_i = i;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span>            last_j = j;</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span>            <span class="keywordflow">return</span> value;</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno">  181</span>        }</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        <span class="comment">//old HMG</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        MGStep besti = selectMGVariable(problem,last_i);</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <span class="keywordflow">if</span>(besti.violation == 0.0)</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>        MGStep bestj = selectMGVariable(problem,last_j);</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>        </div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>        <span class="keywordflow">if</span>(bestj.gain &gt; besti.gain){</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>            i = last_j;</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            j = bestj.index;</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>        }<span class="keywordflow">else</span>{</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>            i = last_i;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>            j = besti.index;</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>        }</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>        <span class="keywordflow">if</span> (problem.gradient(i) &lt; problem.gradient(j)) </div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>            std::swap(i, j);</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        last_i = i;</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        last_j = j;</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span>        <span class="keywordflow">return</span> besti.violation;</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>    }</div>
</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>    </div>
<div class="foldopen" id="foldopen00202" data-start="{" data-end="}">
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"><a class="line" href="classshark_1_1_h_m_g_selection_criterion.html#af4b4e8aa1266e0e9f5a7a33f1bd5caf3">  202</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_h_m_g_selection_criterion.html#af4b4e8aa1266e0e9f5a7a33f1bd5caf3">reset</a>(){</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        useLibSVM = <span class="keyword">true</span>;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        smallProblem = <span class="keyword">false</span>;</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>    }</div>
</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>    </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>    <span class="keywordtype">bool</span> isInCorner(Problem <span class="keyword">const</span>&amp; problem)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>        <span class="keywordtype">double</span> Li = problem.boxMin(last_i);</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>        <span class="keywordtype">double</span> Ui = problem.boxMax(last_i);</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        <span class="keywordtype">double</span> Lj = problem.boxMin(last_j);</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span>        <span class="keywordtype">double</span> Uj = problem.boxMax(last_j);</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span>        <span class="keywordtype">double</span> eps_i = 1e-8 * (Ui - Li);</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        <span class="keywordtype">double</span> eps_j = 1e-8 * (Uj - Lj);</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        </div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        <span class="keywordflow">if</span> ((problem.alpha(last_i) &lt;= Li + eps_i || problem.alpha(last_i) &gt;= Ui - eps_i)</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>        &amp;&amp; ((problem.alpha(last_j) &lt;= Lj + eps_j || problem.alpha(last_j) &gt;= Uj - eps_j)))</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>        {</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        }</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>    }</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>    <span class="keyword">struct </span>MGStep{</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span>        std::size_t index;<span class="comment">//index of variable</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span>        <span class="keywordtype">double</span> violation;<span class="comment">//computed gradientValue</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        <span class="keywordtype">double</span> gain;</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    };</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span>    <span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno">  230</span>    MGStep selectMGVariable(Problem&amp; problem,std::size_t i)<span class="keyword"> const</span>{</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        </div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <span class="comment">//best variable pair found so far</span></div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        std::size_t bestIndex = 0;<span class="comment">//index of variable</span></div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        <span class="keywordtype">double</span> bestGain = 0;</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        </div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>        <span class="keywordtype">double</span> largestUp = -1e100;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <span class="keywordtype">double</span> smallestDown = 1e100;</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span> </div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>        <span class="comment">// try combinations with b = old_i</span></div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>        <span class="keyword">typename</span> Problem::QpFloatType* q = problem.quadratic().row(i, 0, problem.active());</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span>        <span class="keywordtype">double</span> ab = problem.alpha(i);</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span>        <span class="keywordtype">double</span> db = problem.diagonal(i);</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>        <span class="keywordtype">double</span> Lb = problem.boxMin(i);</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>        <span class="keywordtype">double</span> Ub = problem.boxMax(i);</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span>        <span class="keywordtype">double</span> gb = problem.gradient(i);</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span>        <span class="keywordflow">for</span> (std::size_t a = 0; a &lt; problem.active(); a++)</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>        {</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span>            <span class="keywordtype">double</span> ga = problem.gradient(a);</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno">  249</span>            </div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno">  250</span>            <span class="keywordflow">if</span> (!problem.isUpperBound(a))</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno">  251</span>                largestUp = std::max(largestUp,ga);</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno">  252</span>            <span class="keywordflow">if</span> (!problem.isLowerBound(a))</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno">  253</span>                smallestDown = std::min(smallestDown,ga);</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno">  254</span>            </div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno">  255</span>            <span class="keywordflow">if</span> (a == i) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno">  256</span>            <span class="comment">//get maximum unconstrained step length</span></div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno">  257</span>            <span class="keywordtype">double</span> denominator = (problem.diagonal(a) + db - 2.0 * q[a]);</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno">  258</span>            <span class="keywordtype">double</span> mu_max = (ga - gb) / denominator;</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno">  259</span>            </div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno">  260</span>            <span class="comment">//check whether a step &gt; 0 is possible at all</span></div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno">  261</span>            <span class="comment">//~ if( mu_max &gt; 0 &amp;&amp; ( problem.isUpperBound(a) || problem.isLowerBound(b)))continue;</span></div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno">  262</span>            <span class="comment">//~ if( mu_max &lt; 0 &amp;&amp; ( problem.isLowerBound(a) || problem.isUpperBound(b)))continue;</span></div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno">  263</span>            </div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno">  264</span>            <span class="comment">//constraint step to box</span></div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno">  265</span>            <span class="keywordtype">double</span> aa = problem.alpha(a);</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno">  266</span>            <span class="keywordtype">double</span> La = problem.boxMin(a);</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno">  267</span>            <span class="keywordtype">double</span> Ua = problem.boxMax(a);</div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno">  268</span>            <span class="keywordtype">double</span> mu_star = mu_max;</div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno">  269</span>            <span class="keywordflow">if</span> (aa + mu_star &lt; La) mu_star = La - aa;</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno">  270</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (mu_star + aa &gt; Ua) mu_star = Ua - aa;</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno">  271</span>            <span class="keywordflow">if</span> (ab - mu_star &lt; Lb) mu_star = ab - Lb;</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno">  272</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (ab - mu_star &gt; Ub) mu_star = ab - Ub;</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno">  273</span> </div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno">  274</span>            <span class="keywordtype">double</span> gain = mu_star * (2.0 * mu_max - mu_star) * denominator;</div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno">  275</span>            </div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno">  276</span>            <span class="comment">// select the largest gain</span></div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno">  277</span>            <span class="keywordflow">if</span> (gain &gt; bestGain)</div>
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno">  278</span>            {</div>
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno">  279</span>                bestGain = gain;</div>
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno">  280</span>                bestIndex = a;</div>
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno">  281</span>            }</div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno">  282</span>        }</div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno">  283</span>        MGStep step;</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno">  284</span>        step.violation= largestUp-smallestDown;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno">  285</span>        step.index = bestIndex;</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno">  286</span>        step.gain=bestGain;</div>
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno">  287</span>        <span class="keywordflow">return</span> step;</div>
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno">  288</span>        </div>
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno">  289</span>    }</div>
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno">  290</span>    </div>
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno">  291</span>    std::size_t last_i;</div>
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno">  292</span>    std::size_t last_j;</div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno">  293</span>    </div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno">  294</span>    <span class="keywordtype">bool</span> useLibSVM;</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno">  295</span>    <span class="keywordtype">bool</span> smallProblem;</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno">  296</span>};</div>
</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno">  297</span> </div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno">  298</span> </div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno">  299</span><span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="foldopen" id="foldopen00300" data-start="{" data-end="};">
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html">  300</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_svm_problem.html">SvmProblem</a>{</div>
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno">  301</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">  302</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> Problem::QpFloatType <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">QpFloatType</a>;</div>
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a4e039c8a44164e2f96137119779ef344">  303</a></span>    <span class="keyword">typedef</span> <span class="keyword">typename</span> Problem::MatrixType <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a4e039c8a44164e2f96137119779ef344">MatrixType</a>;</div>
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#acef7c20b210e81a62d01e9eadd61dc49">  304</a></span>    <span class="keyword">typedef</span> <a class="code hl_struct" href="structshark_1_1_lib_s_v_m_selection_criterion.html" title="Computes the maximum gian solution.">LibSVMSelectionCriterion</a> <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#acef7c20b210e81a62d01e9eadd61dc49">PreferedSelectionStrategy</a>;</div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno">  305</span> </div>
<div class="foldopen" id="foldopen00306" data-start="{" data-end="}">
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#ad10f8907862c01b1fc4ec5cd0ff06823">  306</a></span>    <a class="code hl_function" href="classshark_1_1_svm_problem.html#ad10f8907862c01b1fc4ec5cd0ff06823">SvmProblem</a>(Problem&amp; problem)</div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno">  307</span>    : <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>(problem)</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno">  308</span>    , <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(problem.<a class="code hl_function" href="classshark_1_1_svm_problem.html#afe5c70e6047a13481b3f3dbfbd3b7b4e">linear</a>)</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno">  309</span>    , <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a53377e65ea2637c37acb3f7523a837fc">m_active</a>(problem.<a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>())</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno">  310</span>    , <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>(problem.<a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>(),<a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a28e0b952dcae83b045ba488526875f3c">AlphaFree</a>){</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno">  311</span>        <span class="comment">//compute the gradient if alpha != 0</span></div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno">  312</span>        <span class="keywordflow">for</span> (std::size_t i=0; i != <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>(); i++){</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno">  313</span>            <span class="keywordtype">double</span> v = <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(i);</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno">  314</span>            <span class="keywordflow">if</span> (v != 0.0){</div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno">  315</span>                <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">QpFloatType</a>* q = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e" title="representation of the quadratic part of the objective function">quadratic</a>().row(i, 0, <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno">  316</span>                <span class="keywordflow">for</span> (std::size_t a=0; a &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>(); a++) </div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno">  317</span>                    <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(a) -= q[a] * v;</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno">  318</span>            }</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno">  319</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(i);</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno">  320</span>        }</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno">  321</span>    }</div>
</div>
<div class="foldopen" id="foldopen00322" data-start="{" data-end="}">
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">  322</a></span>    std::size_t <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno">  323</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.dimensions();</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno">  324</span>    }</div>
</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno">  325</span> </div>
<div class="foldopen" id="foldopen00326" data-start="{" data-end="}">
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">  326</a></span>    std::size_t <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno">  327</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a53377e65ea2637c37acb3f7523a837fc">m_active</a>;</div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno">  328</span>    }</div>
</div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno">  329</span> </div>
<div class="foldopen" id="foldopen00330" data-start="{" data-end="}">
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aeb63064bffd6c4f4ff157a45535bb142">  330</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#aeb63064bffd6c4f4ff157a45535bb142">boxMin</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno">  331</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i]==<a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a58dcbef75d88f882ee2072dbc57c6fad">AlphaDeactivated</a>? <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(i): <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.boxMin(i);</div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno">  332</span>    }</div>
</div>
<div class="foldopen" id="foldopen00333" data-start="{" data-end="}">
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#afc78269e1b3b3f0372018eb3172db25e">  333</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#afc78269e1b3b3f0372018eb3172db25e">boxMax</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno">  334</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i]==<a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a58dcbef75d88f882ee2072dbc57c6fad">AlphaDeactivated</a>? <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(i): <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.boxMax(i);</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno">  335</span>    }</div>
</div>
<div class="foldopen" id="foldopen00336" data-start="{" data-end="}">
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a39babf310726215d71ef6e29235342c9">  336</a></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a39babf310726215d71ef6e29235342c9">isLowerBound</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno">  337</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] &amp; <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02aba725b5f89015335eeea5ee054dae747">AlphaLowerBound</a>;</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno">  338</span>    }</div>
</div>
<div class="foldopen" id="foldopen00339" data-start="{" data-end="}">
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#ab02d8e8ba4ed8d48ba32fed34c6a1247">  339</a></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#ab02d8e8ba4ed8d48ba32fed34c6a1247">isUpperBound</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno">  340</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] &amp; <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02ab7f64265c75300658e04dfbc2ae28db5">AlphaUpperBound</a>;</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno">  341</span>    }</div>
</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno">  342</span><span class="comment"></span> </div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno">  343</span><span class="comment">    /// representation of the quadratic part of the objective function</span></div>
<div class="foldopen" id="foldopen00344" data-start="{" data-end="}">
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e">  344</a></span><span class="comment"></span>    <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a4e039c8a44164e2f96137119779ef344">MatrixType</a>&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e" title="representation of the quadratic part of the objective function">quadratic</a>(){</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno">  345</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.quadratic;</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno">  346</span>    }</div>
</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno">  347</span> </div>
<div class="foldopen" id="foldopen00348" data-start="{" data-end="}">
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#afe5c70e6047a13481b3f3dbfbd3b7b4e">  348</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#afe5c70e6047a13481b3f3dbfbd3b7b4e">linear</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno">  349</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.linear(i);</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno">  350</span>    }</div>
</div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno">  351</span> </div>
<div class="foldopen" id="foldopen00352" data-start="{" data-end="}">
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">  352</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno">  353</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i);</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno">  354</span>    }</div>
</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno">  355</span> </div>
<div class="foldopen" id="foldopen00356" data-start="{" data-end="}">
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aa8f67d9116f73ddd35faf9f16d13e39f">  356</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#aa8f67d9116f73ddd35faf9f16d13e39f">diagonal</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno">  357</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.diagonal(i);</div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno">  358</span>    }</div>
</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno">  359</span> </div>
<div class="foldopen" id="foldopen00360" data-start="{" data-end="}">
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">  360</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno">  361</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i);</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno">  362</span>    }</div>
</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno">  363</span>    </div>
<div class="foldopen" id="foldopen00364" data-start="{" data-end="}">
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aac1b3e0a3248593ed5b917940ea8625f">  364</a></span>    std::size_t <a class="code hl_function" href="classshark_1_1_svm_problem.html#aac1b3e0a3248593ed5b917940ea8625f">permutation</a>(std::size_t i)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno">  365</span>        <span class="keywordflow">return</span> <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.permutation[i];</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno">  366</span>    }</div>
</div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno">  367</span> </div>
<div class="foldopen" id="foldopen00368" data-start="{" data-end="}">
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#acb8152953435a41f851793490341d4c3">  368</a></span>    RealVector <a class="code hl_function" href="classshark_1_1_svm_problem.html#acb8152953435a41f851793490341d4c3">getUnpermutedAlpha</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno">  369</span>        RealVector <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno">  370</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;<a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>(); i++) </div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno">  371</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(<a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.permutation[i]) = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i);</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno">  372</span>        <span class="keywordflow">return</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>;</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno">  373</span>    }</div>
</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno">  374</span><span class="comment"></span> </div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno">  375</span><span class="comment">    ///\brief Does an update of SMO given a working set with indices i and j.</span></div>
<div class="foldopen" id="foldopen00376" data-start="{" data-end="}">
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a31367cdd5b8129925a6c0e70515b4e0d">  376</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a31367cdd5b8129925a6c0e70515b4e0d" title="Does an update of SMO given a working set with indices i and j.">updateSMO</a>(std::size_t i, std::size_t j){</div>
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno">  377</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(i &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno">  378</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(j &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno">  379</span>        <span class="comment">// get the matrix row corresponding to the first variable of the working set</span></div>
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno">  380</span>        <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">QpFloatType</a>* qi = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e" title="representation of the quadratic part of the objective function">quadratic</a>().row(i, 0, <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00381" name="l00381"></a><span class="lineno">  381</span> </div>
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno">  382</span>        <span class="comment">// solve the sub-problem defined by i and j</span></div>
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno">  383</span>        <span class="keywordtype">double</span> numerator = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(i) - <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(j);</div>
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno">  384</span>        <span class="keywordtype">double</span> denominator = <a class="code hl_function" href="classshark_1_1_svm_problem.html#aa8f67d9116f73ddd35faf9f16d13e39f">diagonal</a>(i) + <a class="code hl_function" href="classshark_1_1_svm_problem.html#aa8f67d9116f73ddd35faf9f16d13e39f">diagonal</a>(j) - 2.0 * qi[j];</div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno">  385</span>        denominator =  std::max(denominator,1.e-12);</div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno">  386</span>        <span class="keywordtype">double</span> step = numerator/denominator;</div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno">  387</span>            </div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno">  388</span>        <span class="comment">//update alpha in a numerically stable way</span></div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno">  389</span>        <span class="comment">// do the update of the alpha values carefully - avoid numerical problems</span></div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno">  390</span>        <span class="keywordtype">double</span> Ui = <a class="code hl_function" href="classshark_1_1_svm_problem.html#afc78269e1b3b3f0372018eb3172db25e">boxMax</a>(i);</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno">  391</span>        <span class="keywordtype">double</span> Lj = <a class="code hl_function" href="classshark_1_1_svm_problem.html#aeb63064bffd6c4f4ff157a45535bb142">boxMin</a>(j);</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno">  392</span>        <span class="keywordtype">double</span> aiOld = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i);</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno">  393</span>        <span class="keywordtype">double</span> ajOld = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(j);</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno">  394</span>        <span class="keywordtype">double</span>&amp; ai = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i);</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno">  395</span>        <span class="keywordtype">double</span>&amp; aj = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(j);</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno">  396</span>        <span class="keywordflow">if</span> (step &gt;= std::min(Ui - ai, aj - Lj))</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno">  397</span>        {</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno">  398</span>            <span class="keywordflow">if</span> (Ui - ai &gt; aj - Lj)</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno">  399</span>            {</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno">  400</span>                step = aj - Lj;</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno">  401</span>                ai += step;</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno">  402</span>                aj = Lj;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno">  403</span>            }</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno">  404</span>            <span class="keywordflow">else</span> <span class="keywordflow">if</span> (Ui - ai &lt; aj - Lj)</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno">  405</span>            {</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno">  406</span>                step = Ui - ai;</div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno">  407</span>                ai = Ui;</div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno">  408</span>                aj -= step;</div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno">  409</span>            }</div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno">  410</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno">  411</span>            {</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno">  412</span>                step = Ui - ai;</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno">  413</span>                ai = Ui;</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno">  414</span>                aj = Lj;</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno">  415</span>            }</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno">  416</span>        }</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno">  417</span>        <span class="keywordflow">else</span></div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno">  418</span>        {</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno">  419</span>            ai += step;</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno">  420</span>            aj -= step;</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno">  421</span>        }</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno">  422</span>        </div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno">  423</span>        <span class="keywordflow">if</span>(ai == aiOld &amp;&amp; aj == ajOld)<span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno">  424</span>        </div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno">  425</span>        <span class="comment">//Update internal data structures (gradient and alpha status)</span></div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno">  426</span>        <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">QpFloatType</a>* qj = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e" title="representation of the quadratic part of the objective function">quadratic</a>().row(j, 0, <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno">  427</span>        <span class="keywordflow">for</span> (std::size_t a = 0; a &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>(); a++) </div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno">  428</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(a) -= step * qi[a] - step * qj[a];</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno">  429</span>        </div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno">  430</span>        <span class="comment">//update boundary status</span></div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno">  431</span>        <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(i);</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno">  432</span>        <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(j);</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno">  433</span>    }</div>
</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno">  434</span><span class="comment"></span> </div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno">  435</span><span class="comment">    ///\brief Returns the current function value of the problem.</span></div>
<div class="foldopen" id="foldopen00436" data-start="{" data-end="}">
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aff44e8756f1ce22489ff00bdb25cb95d">  436</a></span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#aff44e8756f1ce22489ff00bdb25cb95d" title="Returns the current function value of the problem.">functionValue</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno">  437</span>        <span class="keywordflow">return</span> 0.5*inner_prod(<a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>+<a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.linear,<a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha);</div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno">  438</span>    }</div>
</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno">  439</span> </div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aa98f2e4bcbd2311dd36f1c28ade75bd2">  440</a></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#aa98f2e4bcbd2311dd36f1c28ade75bd2">shrink</a>(<span class="keywordtype">double</span>){<span class="keywordflow">return</span> <span class="keyword">false</span>;}</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a073a4ac3cd7dddbd840fe8b38ca2b399">  441</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a073a4ac3cd7dddbd840fe8b38ca2b399">reshrink</a>(){}</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#ad1472ef03326d4e0d8a98f4a3d7e159a">  442</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#ad1472ef03326d4e0d8a98f4a3d7e159a">unshrink</a>(){}</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno">  443</span><span class="comment"></span> </div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno">  444</span><span class="comment">    /// \brief Define the initial solution for the iterative solver.</span></div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno">  445</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno">  446</span><span class="comment">    /// This method can be used to warm-start the solver. It requires a</span></div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno">  447</span><span class="comment">    /// feasible solution (alpha) and the corresponding gradient of the</span></div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno">  448</span><span class="comment">    /// dual objective function.</span></div>
<div class="foldopen" id="foldopen00449" data-start="{" data-end="}">
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aa19eecb264f01e1e3f8aa07640004d7b">  449</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#aa19eecb264f01e1e3f8aa07640004d7b" title="Define the initial solution for the iterative solver.">setInitialSolution</a>(RealVector <span class="keyword">const</span>&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>, RealVector <span class="keyword">const</span>&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>)</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno">  450</span>    {</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno">  451</span>        std::size_t n = <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>();</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno">  452</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>.size() == n);</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno">  453</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>.size() == n);</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno">  454</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;n; i++)</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno">  455</span>        {</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno">  456</span>            std::size_t j = <a class="code hl_function" href="classshark_1_1_svm_problem.html#aac1b3e0a3248593ed5b917940ea8625f">permutation</a>(i);</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno">  457</span>            <a class="code hl_define" href="_exception_8h.html#a73abb5049a0168d72a48e72dda41708b">SHARK_ASSERT</a>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(j) &gt;= <a class="code hl_function" href="classshark_1_1_svm_problem.html#aeb63064bffd6c4f4ff157a45535bb142">boxMin</a>(j) &amp;&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(j) &lt;= <a class="code hl_function" href="classshark_1_1_svm_problem.html#afc78269e1b3b3f0372018eb3172db25e">boxMax</a>(j));</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno">  458</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i) = <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(j);</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno">  459</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i) = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(j);</div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno">  460</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(i);</div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno">  461</span>        }</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno">  462</span>    }</div>
</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno">  463</span><span class="comment"></span> </div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno">  464</span><span class="comment">    /// \brief Define the initial solution for the iterative solver.</span></div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno">  465</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno">  466</span><span class="comment">    /// This method can be used to warm-start the solver. It requires a</span></div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno">  467</span><span class="comment">    /// feasible solution (alpha), for which it computes the gradient of</span></div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno">  468</span><span class="comment">    /// the dual objective function. Note that this is a quadratic time</span></div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno">  469</span><span class="comment">    /// operation in the number of non-zero coefficients.</span></div>
<div class="foldopen" id="foldopen00470" data-start="{" data-end="}">
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a21e030b9a4e898dd8ca16f555cad4447">  470</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a21e030b9a4e898dd8ca16f555cad4447" title="Define the initial solution for the iterative solver.">setInitialSolution</a>(RealVector <span class="keyword">const</span>&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>)</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno">  471</span>    {</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno">  472</span>        std::size_t n = <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>();</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno">  473</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>.size() == n);</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno">  474</span>        RealVector <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a> = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.linear;</div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno">  475</span>        blas::vector&lt;QpFloatType&gt; q(n);</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno">  476</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;n; i++)</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno">  477</span>        {</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno">  478</span>            <span class="keywordtype">double</span> a = <a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(i);</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno">  479</span>            <span class="keywordflow">if</span> (a == 0.0) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno">  480</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.quadratic.row(i, 0, n, q.storage());</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno">  481</span>            noalias(<a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>) -= a * q;</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno">  482</span>        }</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno">  483</span>        <a class="code hl_function" href="classshark_1_1_svm_problem.html#aa19eecb264f01e1e3f8aa07640004d7b" title="Define the initial solution for the iterative solver.">setInitialSolution</a>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>, <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>);</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno">  484</span>    }</div>
</div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno">  485</span>    <span class="comment"></span></div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno">  486</span><span class="comment">    ///\brief Remove the i-th example from the problem while taking the equality constraint into account.</span></div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno">  487</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno">  488</span><span class="comment">    /// The i-th element is first set to zero and as well as an unspecified set corrected so</span></div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno">  489</span><span class="comment">    /// that the constraint is fulfilled.</span></div>
<div class="foldopen" id="foldopen00490" data-start="{" data-end="}">
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a218c29273fd1258c287357a1b0493918">  490</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a218c29273fd1258c287357a1b0493918" title="Remove the i-th example from the problem while taking the equality constraint into account.">deactivateVariable</a>(std::size_t i){</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno">  491</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(i &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno">  492</span>        <span class="comment">//we need to correct for the equality constraint</span></div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno">  493</span>        <span class="comment">//that means we have to move enough variables to satisfy the constraint again.</span></div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno">  494</span>        <span class="keywordflow">for</span> (std::size_t j=0; j&lt;<a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>(); j++){</div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno">  495</span>            <span class="keywordflow">if</span> (j == i || <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[j] == <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a58dcbef75d88f882ee2072dbc57c6fad">AlphaDeactivated</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno">  496</span>            <span class="comment">//propose the maximum step possible and let applyStep cut it down.</span></div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno">  497</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#aca60a43765c528fb1e2e5a5acb495de8" title="Update the problem by a proposed step i taking the box constraints into account.">applyStep</a>(i,j, -<a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(i));</div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno">  498</span>            <span class="keywordflow">if</span>(<a class="code hl_function" href="classshark_1_1_svm_problem.html#a97a8afab15ad38ec1fb321317f9454a1">alpha</a>(i) == 0.0) <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno">  499</span>        }</div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno">  500</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] = <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a58dcbef75d88f882ee2072dbc57c6fad">AlphaDeactivated</a>;</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno">  501</span>    }<span class="comment"></span></div>
</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno">  502</span><span class="comment">    ///\brief Reactivate an previously deactivated variable.</span></div>
<div class="foldopen" id="foldopen00503" data-start="{" data-end="}">
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a0c80f38017ca75c1b2a6bc3654e0b627">  503</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a0c80f38017ca75c1b2a6bc3654e0b627" title="Reactivate an previously deactivated variable.">activateVariable</a>(std::size_t i){</div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno">  504</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(i &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno">  505</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] = <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a28e0b952dcae83b045ba488526875f3c">AlphaFree</a>;</div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno">  506</span>        <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(i);</div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno">  507</span>    }</div>
</div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno">  508</span>    <span class="comment"></span></div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno">  509</span><span class="comment">    /// exchange two variables via the permutation</span></div>
<div class="foldopen" id="foldopen00510" data-start="{" data-end="}">
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a2906035d35c845bde74e931a3b7b57d0">  510</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a2906035d35c845bde74e931a3b7b57d0" title="exchange two variables via the permutation">flipCoordinates</a>(std::size_t i, std::size_t j)</div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno">  511</span>    {</div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno">  512</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(i &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno">  513</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(j &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno">  514</span>        <span class="keywordflow">if</span> (i == j) <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno">  515</span> </div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno">  516</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.flipCoordinates(i, j);</div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno">  517</span>        std::swap( <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>[i], <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>[j]);</div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno">  518</span>        std::swap( <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i], <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[j]);</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno">  519</span>    }</div>
</div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno">  520</span>    <span class="comment"></span></div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno">  521</span><span class="comment">    /// \brief Scales all box constraints by a constant factor and adapts the solution using a separate scaling</span></div>
<div class="foldopen" id="foldopen00522" data-start="{" data-end="}">
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a0390d19fab99eb4c47afd40ce22deb81">  522</a></span><span class="comment"></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a0390d19fab99eb4c47afd40ce22deb81" title="Scales all box constraints by a constant factor and adapts the solution using a separate scaling.">scaleBoxConstraints</a>(<span class="keywordtype">double</span> factor, <span class="keywordtype">double</span> variableScalingFactor){</div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno">  523</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.scaleBoxConstraints(factor,variableScalingFactor);</div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno">  524</span>        <span class="keywordflow">for</span>(std::size_t i = 0; i != this-&gt;<a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>(); ++i){</div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno">  525</span>            <span class="comment">//don&#39;t change deactivated variables</span></div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno">  526</span>            <span class="keywordflow">if</span>(<a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] == <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a58dcbef75d88f882ee2072dbc57c6fad">AlphaDeactivated</a>) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno">  527</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i) -= <a class="code hl_function" href="classshark_1_1_svm_problem.html#afe5c70e6047a13481b3f3dbfbd3b7b4e">linear</a>(i);</div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno">  528</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i) *= variableScalingFactor;</div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno">  529</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i) += <a class="code hl_function" href="classshark_1_1_svm_problem.html#afe5c70e6047a13481b3f3dbfbd3b7b4e">linear</a>(i);</div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno">  530</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(i);</div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno">  531</span>        }</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno">  532</span>    }</div>
</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno">  533</span>    <span class="comment"></span></div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno">  534</span><span class="comment">    /// \brief adapts the linear part of the problem and updates the internal data structures accordingly.</span></div>
<div class="foldopen" id="foldopen00535" data-start="{" data-end="}">
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a9b1278df58fcf906b5395793f5bf1b33">  535</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a9b1278df58fcf906b5395793f5bf1b33" title="adapts the linear part of the problem and updates the internal data structures accordingly.">setLinear</a>(std::size_t i, <span class="keywordtype">double</span> newValue){</div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno">  536</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i) -= <a class="code hl_function" href="classshark_1_1_svm_problem.html#afe5c70e6047a13481b3f3dbfbd3b7b4e">linear</a>(i);</div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno">  537</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(i) += newValue;</div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno">  538</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.linear(i) = newValue;</div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno">  539</span>    }</div>
</div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno">  540</span>    </div>
<div class="foldopen" id="foldopen00541" data-start="{" data-end="}">
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a33eaf27af1bb982dcd7f965fcfbce884">  541</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#a33eaf27af1bb982dcd7f965fcfbce884">checkKKT</a>()<span class="keyword">const</span>{</div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno">  542</span>        <span class="keywordtype">double</span> largestUp = -1e100;</div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno">  543</span>        <span class="keywordtype">double</span> smallestDown = 1e100;</div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno">  544</span>        <span class="keywordflow">for</span> (std::size_t a = 0; a &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>(); a++){</div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno">  545</span>            <span class="keywordflow">if</span> (!<a class="code hl_function" href="classshark_1_1_svm_problem.html#a39babf310726215d71ef6e29235342c9">isLowerBound</a>(a))</div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno">  546</span>                smallestDown = std::min(smallestDown,<a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(a));</div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno">  547</span>            <span class="keywordflow">if</span> (!<a class="code hl_function" href="classshark_1_1_svm_problem.html#ab02d8e8ba4ed8d48ba32fed34c6a1247">isUpperBound</a>(a))</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno">  548</span>                largestUp = std::max(largestUp,<a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(a));</div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno">  549</span>        }</div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno">  550</span>        <span class="keywordflow">return</span> largestUp - smallestDown;</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno">  551</span>    }</div>
</div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno">  552</span> </div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno">  553</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">  554</a></span>    Problem <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>;</div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno">  555</span><span class="comment"></span> </div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno">  556</span><span class="comment">    /// gradient of the objective function at the current alpha</span></div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c">  557</a></span><span class="comment"></span>    RealVector <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>;  </div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno">  558</span> </div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a53377e65ea2637c37acb3f7523a837fc">  559</a></span>    std::size_t <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a53377e65ea2637c37acb3f7523a837fc">m_active</a>; </div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno">  560</span><span class="comment"></span> </div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno">  561</span><span class="comment">    /// \brief Stores the status, whther alpha is on the lower or upper bound, or whether it is free.</span></div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b">  562</a></span><span class="comment"></span>    std::vector&lt;char&gt; <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>;</div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno">  563</span><span class="comment"></span> </div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno">  564</span><span class="comment">    ///\brief Update the problem by a proposed step i taking the box constraints into account.</span></div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno">  565</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno">  566</span><span class="comment">    /// A step length 0&lt;=lambda&lt;=1 is found so that </span></div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno">  567</span><span class="comment">    /// boxMin(i) &lt;= alpha(i)+lambda*step &lt;= boxMax(i) </span></div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno">  568</span><span class="comment">    /// and</span></div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno">  569</span><span class="comment">    /// boxMin(j) &lt;= alpha(j)-lambda*step &lt;= boxMax(j)</span></div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno">  570</span><span class="comment">    /// the update is performed in a numerically stable way and the internal data structures</span></div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno">  571</span><span class="comment">    /// are also updated.</span></div>
<div class="foldopen" id="foldopen00572" data-start="{" data-end="}">
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#aca60a43765c528fb1e2e5a5acb495de8">  572</a></span><span class="comment"></span>    <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#aca60a43765c528fb1e2e5a5acb495de8" title="Update the problem by a proposed step i taking the box constraints into account.">applyStep</a>(std::size_t i, std::size_t j, <span class="keywordtype">double</span> step){</div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno">  573</span>            <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(i &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno">  574</span>            <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(j &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno">  575</span>            <span class="comment">// do the update of the alpha values carefully - avoid numerical problems</span></div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno">  576</span>            <span class="keywordtype">double</span> Ui = <a class="code hl_function" href="classshark_1_1_svm_problem.html#afc78269e1b3b3f0372018eb3172db25e">boxMax</a>(i);</div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno">  577</span>            <span class="keywordtype">double</span> Lj = <a class="code hl_function" href="classshark_1_1_svm_problem.html#aeb63064bffd6c4f4ff157a45535bb142">boxMin</a>(j);</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno">  578</span>            <span class="keywordtype">double</span> aiOld = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i);</div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno">  579</span>            <span class="keywordtype">double</span> ajOld = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(j);</div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno">  580</span>            <span class="keywordtype">double</span>&amp; ai = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i);</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno">  581</span>            <span class="keywordtype">double</span>&amp; aj = <a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(j);</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno">  582</span>            <span class="keywordflow">if</span> (step &gt;= std::min(Ui - ai, aj - Lj))</div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno">  583</span>            {</div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno">  584</span>                    <span class="keywordflow">if</span> (Ui - ai &gt; aj - Lj)</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno">  585</span>                    {</div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno">  586</span>                            step = aj - Lj;</div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno">  587</span>                            ai += step;</div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno">  588</span>                            aj = Lj;</div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno">  589</span>                    }</div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno">  590</span>                    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (Ui - ai &lt; aj - Lj)</div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno">  591</span>                    {</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno">  592</span>                            step = Ui - ai;</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno">  593</span>                            ai = Ui;</div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno">  594</span>                            aj -= step;</div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno">  595</span>                    }</div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno">  596</span>                    <span class="keywordflow">else</span></div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno">  597</span>                    {</div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno">  598</span>                            step = Ui - ai;</div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno">  599</span>                            ai = Ui;</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno">  600</span>                            aj = Lj;</div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno">  601</span>                    }</div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno">  602</span>            }</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno">  603</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno">  604</span>            {</div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno">  605</span>                    ai += step;</div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno">  606</span>                    aj -= step;</div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno">  607</span>            }</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno">  608</span>            </div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno">  609</span>            <span class="keywordflow">if</span>(ai == aiOld &amp;&amp; aj == ajOld)<span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno">  610</span>            </div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno">  611</span>            <span class="comment">//Update internal data structures (gradient and alpha status)</span></div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno">  612</span>            <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">QpFloatType</a>* qi = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e" title="representation of the quadratic part of the objective function">quadratic</a>().row(i, 0, <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno">  613</span>            <a class="code hl_typedef" href="classshark_1_1_svm_problem.html#a36f9963fc67abd79168cc9bcbaf98b6c">QpFloatType</a>* qj = <a class="code hl_function" href="classshark_1_1_svm_problem.html#ac12ebec3daaab85111af6dd0561e993e" title="representation of the quadratic part of the objective function">quadratic</a>().row(j, 0, <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>());</div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno">  614</span>            <span class="keywordflow">for</span> (std::size_t a = 0; a &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a1e36b705c5de7db9cc1a9882753d8102">active</a>(); a++) </div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno">  615</span>                    <a class="code hl_variable" href="classshark_1_1_svm_problem.html#abe3da8520eacc5b4c5c5f1b051ad726c" title="gradient of the objective function at the current alpha">m_gradient</a>(a) -= step * qi[a] - step * qj[a];</div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno">  616</span>            </div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno">  617</span>            <span class="comment">//update boundary status</span></div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno">  618</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(i);</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno">  619</span>            <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(j);</div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno">  620</span>    }</div>
</div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno">  621</span> </div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno">  622</span>    </div>
<div class="foldopen" id="foldopen00623" data-start="{" data-end="}">
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">  623</a></span>    <span class="keywordtype">void</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#ade0b5d8577fdb5fde149f542babc1369">updateAlphaStatus</a>(std::size_t i){</div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno">  624</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(i &lt; <a class="code hl_function" href="classshark_1_1_svm_problem.html#a42f4bb52a5e7c0415519da0ecf060edf">dimensions</a>());</div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno">  625</span>        <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] = <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02a28e0b952dcae83b045ba488526875f3c">AlphaFree</a>;</div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno">  626</span>        <span class="keywordflow">if</span>(<a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i) == <a class="code hl_function" href="classshark_1_1_svm_problem.html#afc78269e1b3b3f0372018eb3172db25e">boxMax</a>(i))</div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno">  627</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] |= <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02ab7f64265c75300658e04dfbc2ae28db5">AlphaUpperBound</a>;</div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno">  628</span>        <span class="keywordflow">if</span>(<a class="code hl_variable" href="classshark_1_1_svm_problem.html#adb2ad6ad0ad2571b0985f767347223d3">m_problem</a>.alpha(i) == <a class="code hl_function" href="classshark_1_1_svm_problem.html#aeb63064bffd6c4f4ff157a45535bb142">boxMin</a>(i))</div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno">  629</span>            <a class="code hl_variable" href="classshark_1_1_svm_problem.html#a37d6169989efa917c76435eb50167a7b" title="Stores the status, whther alpha is on the lower or upper bound, or whether it is free.">m_alphaStatus</a>[i] |= <a class="code hl_enumvalue" href="namespaceshark.html#a51a13ac7e3cbd1f789124f6f132e5d02aba725b5f89015335eeea5ee054dae747">AlphaLowerBound</a>;</div>
<div class="line"><a id="l00630" name="l00630"></a><span class="lineno">  630</span>    }</div>
</div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno">  631</span>    </div>
<div class="foldopen" id="foldopen00632" data-start="{" data-end="}">
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_problem.html#abb9d0ed983afddf9bcc3b856c8b04b02">  632</a></span>    <span class="keywordtype">bool</span> <a class="code hl_function" href="classshark_1_1_svm_problem.html#abb9d0ed983afddf9bcc3b856c8b04b02">testShrinkVariable</a>(std::size_t a, <span class="keywordtype">double</span> largestUp, <span class="keywordtype">double</span> smallestDown)<span class="keyword">const</span>{</div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno">  633</span>        <span class="keywordflow">if</span> (</div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno">  634</span>            ( <a class="code hl_function" href="classshark_1_1_svm_problem.html#a39babf310726215d71ef6e29235342c9">isLowerBound</a>(a) &amp;&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(a) &lt; smallestDown)</div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno">  635</span>            || ( <a class="code hl_function" href="classshark_1_1_svm_problem.html#ab02d8e8ba4ed8d48ba32fed34c6a1247">isUpperBound</a>(a) &amp;&amp; <a class="code hl_function" href="classshark_1_1_svm_problem.html#ae638f4ac4dba40b797e5f6cfd2244c77">gradient</a>(a) &gt;largestUp)</div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno">  636</span>        ){</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno">  637</span>            <span class="comment">// In this moment no feasible step including this variable</span></div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno">  638</span>            <span class="comment">// can improve the objective. Thus deactivate the variable.</span></div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno">  639</span>            <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno">  640</span>        }</div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno">  641</span>        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno">  642</span>    }</div>
</div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno">  643</span>};</div>
</div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno">  644</span> </div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno">  645</span><span class="keyword">template</span>&lt;<span class="keyword">class</span> Problem&gt;</div>
<div class="foldopen" id="foldopen00646" data-start="{" data-end="};">
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_shrinking_problem.html">  646</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_svm_shrinking_problem.html">SvmShrinkingProblem</a>: <span class="keyword">public</span> <a class="code hl_struct" href="structshark_1_1_box_based_shrinking_strategy.html" title="Takes q boxx constrained QP-type problem and implements shrinking on it.">BoxBasedShrinkingStrategy</a>&lt;SvmProblem&lt;Problem&gt; &gt;{</div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno">  647</span><span class="keyword">public</span>:</div>
<div class="foldopen" id="foldopen00648" data-start="{" data-end="}">
<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"><a class="line" href="classshark_1_1_svm_shrinking_problem.html#a520bb3904668c9c62b43aad128ada107">  648</a></span>    <a class="code hl_function" href="classshark_1_1_svm_shrinking_problem.html#a520bb3904668c9c62b43aad128ada107">SvmShrinkingProblem</a>(Problem&amp; problem, <span class="keywordtype">bool</span> <a class="code hl_function" href="structshark_1_1_box_based_shrinking_strategy.html#aaa20fc55d3f28d930e26ca577621c44d">shrink</a>=<span class="keyword">true</span>)</div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno">  649</span>    :<a class="code hl_struct" href="structshark_1_1_box_based_shrinking_strategy.html" title="Takes q boxx constrained QP-type problem and implements shrinking on it.">BoxBasedShrinkingStrategy</a>&lt;<a class="code hl_class" href="classshark_1_1_svm_problem.html">SvmProblem</a>&lt;Problem&gt; &gt;(problem,<a class="code hl_function" href="structshark_1_1_box_based_shrinking_strategy.html#aaa20fc55d3f28d930e26ca577621c44d">shrink</a>){}</div>
</div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno">  650</span>};</div>
</div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno">  651</span> </div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno">  652</span>}</div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno">  653</span><span class="preprocessor">#endif</span></div>
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